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Factorization symmetry in the lattice Boltzmann method

Author

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  • Karlin, Ilya
  • Asinari, Pietro

Abstract

A non-perturbative algebraic theory of the lattice Boltzmann method is developed based on the symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which imposes restricted extension of higher-order Gaussian moments, (ii) A special quasi-equilibrium distribution function found analytically in closed form on the product-lattice in two and three spatial dimensions, and which proves the factorization of quasi-equilibrium moments, and (iii) An algebraic method of pruning based on a one-into-one relation between groups of discrete velocities and moments. Two routes of constructing lattice Boltzmann equilibria are distinguished. The present theory includes previously known limiting and special cases of lattices, and enables automated derivation of lattice Boltzmann models from two-dimensional tables, by finding the roots of one polynomial and solving a few linear systems.

Suggested Citation

  • Karlin, Ilya & Asinari, Pietro, 2010. "Factorization symmetry in the lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1530-1548.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:8:p:1530-1548
    DOI: 10.1016/j.physa.2009.12.032
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    Cited by:

    1. An, Hongyan & Zhang, Chuhua & Meng, Jianping & Zhang, Yonghao, 2012. "Analytical solution of axi-symmetrical lattice Boltzmann model for cylindrical Couette flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 8-14.

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    Keywords

    Kinetic theory; Lattice Boltzmann method;

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